# Correlation between prices or returns?

If you are interested in determining whether there is a correlation between the Federal Reserve Balance Sheet and PPI, would you calculate the correlation between values (prices) or period-to-period change (returns)?

I've massaged both data sets to be of equal length and same date range and have labeled them WWW (WRESCRT) and PPP (PPIACO). Passing them into R we get the following:

> cor(WWW, PPP)
[1] 0.7879144


Then applying the Delt() function:

> PPP.d <- Delt(PPP)


Then applying the na.locf() function:

PPP.D <- na.locf(PPP.d, na.rm=TRUE)


Then passing it through cor() again:

> cor(WWW.D, PPP.D)
[1] -0.406858


So, bottom line is that it matters.

NOTE: To view how I created the data view http://snipt.org/wmkpo. Warning: it needs refactoring but good news is that it's only 27 iines.

• If the period-to-period change shows a correlation, you've shown a correlation between the first derivative (with respect to time) of the two quantities. That's a little different than showing correlation between the values themselves (although I'm guessing there's some relation between the two). – barrycarter Feb 13 '11 at 20:55
• WRT your bottom line: don't forget that you now have quantitative easing, which you should consider as a structural break in the model. Using only data up to 2007 I get a correlation of only -0.1524359 – Owe Jessen Feb 14 '11 at 14:50
• The blog post: portfolioprobe.com/2011/01/12/the-number-1-novice-quant-mistake shows (and tries to explain) why you generally want to use returns and not prices. – Patrick Burns Feb 14 '11 at 19:01
• Clicking the link I get "The resource you are looking for has been removed, had its name changed, or is temporarily unavailable." – vonjd Jun 28 '18 at 15:44